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# One-Way and Factorial ANOVA - PowerPoint PPT Presentation

One-Way and Factorial ANOVA. SPSS Lab #3. One-Way ANOVA. Two ways to run a one-way ANOVA Analyze  Compare Means  One-Way ANOVA Use if you have multiple DV’s, but only one IV Analyze  General Linear Model  Univariate Use if you have only one DV bc/ can provide effect size statistics

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### One-Way and Factorial ANOVA

SPSS Lab #3

• Two ways to run a one-way ANOVA

• Analyze  Compare Means  One-Way ANOVA

• Use if you have multiple DV’s, but only one IV

• Analyze  General Linear Model  Univariate

• Use if you have only one DV bc/ can provide effect size statistics

• More on this later (factorial ANOVA section)

• First we have to test if we meet the assumptions of ANOVA:

• Independence of Observations

• Cannot be tested statistically, is determined by research methodology only

• Normally Distributed Data

• Shapiro-Wilk’s W statistic, if significant, indicates significant non-normality in data

• Analyze  Descriptive Statistics  Explore

• Click on “Plots”, make sure “Normality Plots w/Tests” is checked

• Homogeneity of Variances (Homoscedasticity)

• Tested at the same time you test ANOVA

• Analyze  Compare Means  One-Way ANOVA

• Click on “Options” and make sure “Homogeneity of variance test” is checked

• If violated, use Brown-Forsythe or Welch statistics, which do not assume homoscedasticity

• One-Way ANOVA

• Analyze  Compare Means  One-Way ANOVA

• “Dependent List” = DV’s; “Factor” = IV

• Options

• Descriptive

• Fixed and random effects

• Homogeneity of variance test

• Levene’s Test: Significant result  Non-homogenous variances

• Brown-Forsythe

• Welch

• Means plot

• One-Way ANOVA

• Post-Hoc

• Can only be done if your IV has 3+ levels

• Pointless if only 2 levels, just look @ the means

• Click the test you want, either with equal variances assumed or not assumed

• DON’T just click all of them and see which one gives what you want (that’s cheating), select the test you want priori

• Contrasts

• Click “Polynomial”, Leave “Degree” at default (“Linear”)

• # of coefficients should equal # of levels of your IV

• Doesn’t count missing cells, so if you have 3 levels, but no one in one of the levels, you should have 2 coefficients

• Coefficients need to sum to 0

• Contrasts

• IV = Race – 1=Caucasian, 2=African American, 3=Asian American, 4=Hispanic, 5=Native American, 6=Other, BUT there were no Native Americans in the sample

• If you want to compare Caucasians to “Other”, coefficients = 1, 0, 0, 0, -1

• Caucasians vs. everyone else = -1, .25, .25, .25, .25

• Univariate works for both one-way (1 IV) and factorial ANOVA’s (2+ IV’s)

• Allows for specification of both fixed and random factors (IV’s)

• Assumptions

• Independence of Observations

• Normally Distributed Data

• Both same as one-way ANOVA

• Assumptions:

• Homoscedasticity

• Tested at the same time you test ANOVA

• Click on Analyze  General Linear Model  Univariate

• Click on “Options” and make sure “Homogeneity tests” is checked

• Options

• Estimated Marginal Means

• Displays means, SD’s, & CI’s for each level of each IV selected

• If “Compare main effects” is checked, works as one-way ANOVA on each IV selected

• “Confidence interval adjustments” allows you to correct for inflation of alpha using Bonferroni or Sidak method

• Descriptive statistics

• Estimates of effect size

• Observed power

• Pointless, adds nothing to interpretation of p-value and e.s.

• Homogeneity tests

• Levene’s test

• Save

• Post Hoc

• Select the IV for which you wish to compare all levels against all other levels (i.e. that you don’t plan to do planned comparisons on)

• Click on the right arrow button so the IV is in the box labeled “Post Hoc Tests for”

• Check the post hoc tests you want done, either with equal variances assumed or not assumed

• Click “Continue”

• Plots

• Horizontal Axis

• What IV is on the x-axis

• Separate Lines

• Separate Plots

• The following graph has the IV “Race” on the horizontal axis and separate lines by the IV “Gender”

• Model

• Allows you to:

• Denote which main effects and interactions you are interested in testing (default is to test ALL of them)

• Specify which type of sum of squares to use

• Usually you won’t be tinkering with this

• Contrasts

• Tests all levels within one IV

• Concern yourself with Simple only for now

• “Reference category” = What level all others are compared to (either first or last, with this referring to how they were numbered)

• Can test specific levels within one IV with specific levels in another IV, but requires knowledge of syntax

• Interpreting interactions

• See graphs